INOUE Tomoki    Department   Undergraduate School  , School of Political Science and Economics    Position   Senior Assistant Professor
Language	English
Publication Date	2021
Type	Academic Journal
Peer Review	Peer reviewed
Title	Coincidence theorem and the inner core
Contribution Type	Sole-authored
Journal	Pure and Applied Functional Analysis
Publisher	Yokohama Publishers
Volume, Issue, Page	6(4),pp.761-775
Total page number	15
Details	We provide two coincidence theorems that are useful mathematical tools for proving the nonemptiness of the inner core. The inner core is a refinement of the core of non-transferable utility (NTU) games. Our first coincidence theorem is a synthesis of Brouwer's fixed point theorem and Debreu and Schmeidler's separation theorem for convex sets. Our second coincidence theorem is a modification of the first one in order for two correspondences to have a nonempty intersection at a strictly positive vector. Inoue's theorem on the nonemptiness of the inner core follows from our first coincidence theorem and an assumption on the efficient surface of payoff vectors for the grand coalition. Our coincidence theorems are suitable for proving the nonemptiness of the inner core in the sense that one of the assumptions in our first coincidence theorem is equivalence to the cardinal balancedness of an NTU game when two correspondences are defined properly.